Question

You are running a race. The probability that you win is 3/5. What is the probability that you lose at most 2 out of your 6 races?

Answer 1

Answer:

The probability that you lose at most 2 out of your 6 races is 0.54432.

Step-by-step explanation:

We are given that you are running a race. The probability that you win is 3/5.

There are total of 6 races.

The above situation can be represented through binomial distribution;

$P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 6 races

            r = number of success = at most 2 lost

            p = probability of success which in our question is probability that

                  you lose a race =  1 - (3/5) = 2/5 or 0.4

Let X = Number of races lost

So, X ~ Binom(n = 6, p = 0.40)

Now, the probability that you lose at most 2 out of your 6 races is given by = P(X $\leq$ 2)

P(X $\leq$ 2)  =  P(X = 0) + P(X = 1) + P(X = 2)

=  $\binom{6}{0} \times 0.40^{0} \times (1-0.40)^{6-0} + \binom{6}{1} \times 0.40^{1} \times (1-0.40)^{6-1} + \binom{6}{2} \times 0.40^{2} \times (1-0.40)^{6-2}$  

=  $1 \times1 \times 0.60^{6} + 6 \times 0.40^{1} \times 0.60^{5} +15\times 0.40^{2} \times 0.60^{4}$  

=  0.54432